Question

The filament temperature of a light bulb is 2 000 K when the bulb delivers 40 W of power.

Answer 1

Answer:

c. 98 W

Explanation:

$P_{i}$ = initial power delivered by bulb at initial temperature = 40 W

$T_{i}$ = initial temperature of filament = 2000 K

Now the temperature of filament of the bulb rises

$P_{f}$ =Final power delivered by bulb at higher temperature

$T_{f}$ = Final higher temperature of filament = 2500 K

As per Stefan's law, the power delivered by the bulb depends directly on fourth power of the temperature. hence we can write

$\frac{P_{f}}{P_{i}} = \frac{T_{f}^{4} }{T_{i}^{4}} \\\frac{P_{f}}{40} = \frac{2500^{4} }{2000^{4}}\\\\P_{f} = (2.44) (40)\\P_{f} = 98 W$